Difference between revisions of "Jackson logarithm"

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[[Jackson logarithm of delta exponential]]<br />
 
[[Jackson logarithm of delta exponential]]<br />
 
[[Delta exponential of Jackson logarithm]]<br />
 
[[Delta exponential of Jackson logarithm]]<br />
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[[Jackson logarithm of a product]]<br />
  
 
=See also=
 
=See also=
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=References=
 
=References=
*{{PaperReference|The time scale logarithm|2008|Billy Jackson|prev=findme|next=findme}}: Definition 1.1, $(1.1)$
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*{{PaperReference|The time scale logarithm|2008|Billy Jackson|next=Jackson logarithm of delta exponential}}: Definition $1.1$, $(1.1)$

Latest revision as of 17:43, 11 February 2017

Let $\mathbb{T}$ be a time scale. Let $p \in \mathcal{R}(\mathbb{T},\mathbb{R})$ be regressive. Let $g \colon \mathbb{T} \rightarrow \mathbb{R}$ be nonvanishing. Define the Jackson logarithm of $g$ by $$\log_{\mathbb{T}}g(t)=\dfrac{g^{\Delta}(t)}{g(t)}.$$

Properties

Jackson logarithm of delta exponential
Delta exponential of Jackson logarithm
Jackson logarithm of a product

See also

Bohner logarithm
Euler-Cauchy logarithm
Mozyrska-Torres logarithm

References